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        <p id="owner"><a name="scalation" class="extype" href="../package.html">scalation</a>.<a name="scalation.minima" class="extype" href="package.html">minima</a></p>
        <h1>ConjugateGradient</h1>
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      <h4 class="signature" id="signature">
      <span class="kind">class</span>
      <span class="symbol"> 
        <span class="name">ConjugateGradient</span>
        
        <span class="result"> extends AnyRef</span>
      </span>
      </h4>
      
          <div class="fullcommenttop" id="comment"><div class="comment cmt"><p>This class solves Non-Linear Programming (NLP) problems using a Conjugate
 Gradient algorithm.  Given a function &quot;f&quot; and a starting point &quot;x&quot;, the
 algorithm computes the gradient and takes steps in the opposite direction.
 In mode 0, the direction is exactly opposite to the gradient (Steepest
 Descent), while modes 1 and 2 set the direction to the following convex
 combination of the current gradient and the previous direction.</p></div><dl class="attributes block"> <dt>See also</dt><dd><span class="cmt"><p>http://www.neos-guide.org/NEOS/index.php/Nonlinear_Conjugate_Gradient_Method</p><p> dir_k = -gradient (x) + beta dir_k-1</p><p> These algorithm iterate until they converges.  Optionally, a constraint
 function &quot;g&quot; may also be given.  The class assumes that partial derivative
 functions are not avialble unless explicitly given via the setDerivatives
 method.</p><p> 0. Steepest-Descent: beta = 0</p><ol class="decimal"><li>Fletcher-Reeves:  beta = square of the ratio gradient norms
 2. Polak-Ribiere:    beta = ratio of dot products</li></ol><p> minimize    f(x)
 subject to  g(x) &lt;= 0
</p></span></dd></dl><div class="toggleContainer block">
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              <h3>Instance Constructors</h3>
              <ol><li visbl="pub" name="scalation.minima.ConjugateGradient#this" data-isabs="false">
      <a id="this:ConjugateGradient"></a>
      <h4 class="signature">
      <span class="kind">new</span>
      <span class="symbol"> 
        <span class="name">ConjugateGradient</span>
        
        <span class="params">(<span name="f">f: FunctionV2S[<span name="scala.Double" class="extype">Double</span>]</span>, <span name="g">g: FunctionV2S[<span name="scala.Double" class="extype">Double</span>]</span>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt"></p><div class="fullcomment"><div class="comment cmt"></div><dl class="paramcmts block"><dt class="param">f</dt><dd class="cmt"><p>the vector-to-scalar objective function</p></dd><dt class="param">g</dt><dd class="cmt"><p>the optional vector-to-scalar constraint function
</p></dd></dl></div>
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      <span class="symbol"> 
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    </li><li visbl="pub" name="scalation.minima.ConjugateGradient#fg" data-isabs="false">
      <a id="fg(VectorD):Double"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">fg</span>
        
        <span class="params">(<span name="x">x: VectorD</span>)</span><span class="result">: <span name="scala.Double" class="extype">Double</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">The objective function f re-scaled by a weighted penalty.</p><div class="fullcomment"><div class="comment cmt"><p>The objective function f re-scaled by a weighted penalty.</p></div><dl class="paramcmts block"><dt class="param">x</dt><dd class="cmt"><p>the coordinate values
</p></dd></dl></div>
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                <span class="name">@throws</span><span class="args">()</span>
              
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    </li><li visbl="pub" name="scalation.minima.ConjugateGradient#fletcherReeves" data-isabs="false">
      <a id="fletcherReeves(VectorD,VectorD):Double"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">fletcherReeves</span>
        
        <span class="params">(<span name="gr1">gr1: VectorD</span>, <span name="gr2">gr2: VectorD</span>)</span><span class="result">: <span name="scala.Double" class="extype">Double</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Set the beta parameter using the Fletcher-Reeves technique.</p><div class="fullcomment"><div class="comment cmt"><p>Set the beta parameter using the Fletcher-Reeves technique.</p></div><dl class="paramcmts block"><dt class="param">gr1</dt><dd class="cmt"><p>the gradient at the previous point</p></dd><dt class="param">gr2</dt><dd class="cmt"><p>the gradient at the current point
</p></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#getClass" data-isabs="false">
      <a id="getClass():java.lang.Class[_]"></a>
      <h4 class="signature">
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      <span class="symbol"> 
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      <a id="hashCode():Int"></a>
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      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">hashCode</span>
        
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        <span class="tparams">[<span name="T0">T0</span>]</span>
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    </li><li visbl="pub" name="scalation.minima.ConjugateGradient#lineSearch" data-isabs="false">
      <a id="lineSearch(VectorD,VectorD):VectorD"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">lineSearch</span>
        
        <span class="params">(<span name="y0">y0: VectorD</span>, <span name="dir">dir: VectorD</span>)</span><span class="result">: VectorD</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Perform a simple Line Search (LS) by making multiple steps in the given
 direction.</p><div class="fullcomment"><div class="comment cmt"><p>Perform a simple Line Search (LS) by making multiple steps in the given
 direction.  Stop when the objective value fails to decrease.</p></div><dl class="paramcmts block"><dt class="param">y0</dt><dd class="cmt"><p>the starting point for the line search</p></dd><dt class="param">dir</dt><dd class="cmt"><p>the given direction vector
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.minima.ConjugateGradient#lineSearchExt" data-isabs="false">
      <a id="lineSearchExt(VectorD,VectorD):VectorD"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">lineSearchExt</span>
        
        <span class="params">(<span name="y0">y0: VectorD</span>, <span name="dir">dir: VectorD</span>)</span><span class="result">: VectorD</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Perform a Line Search (LS) using an &quot;EXTERNAL&quot; Line Search Algorithm,
 (min fg (y0 + dir * z | z in [0, step]).</p><div class="fullcomment"><div class="comment cmt"><p>Perform a Line Search (LS) using an &quot;EXTERNAL&quot; Line Search Algorithm,
 (min fg (y0 + dir * z | z in [0, step]).
 For example, use the Golden Section or Wolfe Search Algorithms.</p></div><dl class="paramcmts block"><dt class="param">y0</dt><dd class="cmt"><p>the starting point for the line search</p></dd><dt class="param">dir</dt><dd class="cmt"><p>the given direction vector
</p></dd></dl></div>
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      <h4 class="signature">
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      <span class="symbol"> 
        <span class="name">ne</span>
        
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      <span class="symbol"> 
        <span class="name">notifyAll</span>
        
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    </li><li visbl="pub" name="scalation.minima.ConjugateGradient#polakRibiere" data-isabs="false">
      <a id="polakRibiere(VectorD,VectorD):Double"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">polakRibiere</span>
        
        <span class="params">(<span name="gr1">gr1: VectorD</span>, <span name="gr2">gr2: VectorD</span>)</span><span class="result">: <span name="scala.Double" class="extype">Double</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Set the beta parameter using the Polak-Ribiere technique.</p><div class="fullcomment"><div class="comment cmt"><p>Set the beta parameter using the Polak-Ribiere technique.</p></div><dl class="paramcmts block"><dt class="param">gr1</dt><dd class="cmt"><p>the gradient at the previous point</p></dd><dt class="param">gr2</dt><dd class="cmt"><p>the gradient at the current point
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.minima.ConjugateGradient#setBeta" data-isabs="false">
      <a id="setBeta(Int):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">setBeta</span>
        
        <span class="params">(<span name="mode">mode: <span name="scala.Int" class="extype">Int</span></span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Set the beta function that is used to determine how much the prior
 search direction is used in determining the new search direction.</p><div class="fullcomment"><div class="comment cmt"><p>Set the beta function that is used to determine how much the prior
 search direction is used in determining the new search direction.</p></div><dl class="paramcmts block"><dt class="param">mode</dt><dd class="cmt"><p>which conjugate gradient technique to use
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.minima.ConjugateGradient#setDerivatives" data-isabs="false">
      <a id="setDerivatives(Array[FunctionV2S[Double]]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">setDerivatives</span>
        
        <span class="params">(<span name="df">df: <span name="scala.Array" class="extype">Array</span>[FunctionV2S[<span name="scala.Double" class="extype">Double</span>]]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Set the partial derivative functions.</p><div class="fullcomment"><div class="comment cmt"><p>Set the partial derivative functions.  If these functions are available,
 they are more efficient and more accurate than estimating the values
 using difference quotients (the default approach).</p></div><dl class="paramcmts block"><dt class="param">df</dt><dd class="cmt"><p>the array of partial derivative functions
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.minima.ConjugateGradient#solve" data-isabs="false">
      <a id="solve(VectorD):(VectorD, Double)"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">solve</span>
        
        <span class="params">(<span name="y">y: VectorD</span>)</span><span class="result">: (VectorD, <span name="scala.Double" class="extype">Double</span>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Solve the Non-Linear Programming problem using a Conjugate Gradient
 algorithm returning the optimal solution x and its objective value f(x).</p><div class="fullcomment"><div class="comment cmt"><p>Solve the Non-Linear Programming problem using a Conjugate Gradient
 algorithm returning the optimal solution x and its objective value f(x).
 Iteratively, compute a gradient and set a search direction as a combination
 of the gradient and the previous direction.  Given a direction, perform
 a Line Search.</p></div><dl class="paramcmts block"><dt class="param">y</dt><dd class="cmt"><p>the starting point
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.minima.ConjugateGradient#steepestDescent" data-isabs="false">
      <a id="steepestDescent(VectorD,VectorD):Double"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">steepestDescent</span>
        
        <span class="params">(<span name="gr1">gr1: VectorD</span>, <span name="gr2">gr2: VectorD</span>)</span><span class="result">: <span name="scala.Double" class="extype">Double</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Set the beta parameter to zero, irregardless (just use the gradient).</p><div class="fullcomment"><div class="comment cmt"><p>Set the beta parameter to zero, irregardless (just use the gradient).</p></div><dl class="paramcmts block"><dt class="param">gr1</dt><dd class="cmt"><p>the gradient at the previous point</p></dd><dt class="param">gr2</dt><dd class="cmt"><p>the gradient at the current point
</p></dd></dl></div>
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        <span class="params">()</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
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        <span class="params">(<span name="arg0">arg0: <span name="scala.Long" class="extype">Long</span></span>, <span name="arg1">arg1: <span name="scala.Int" class="extype">Int</span></span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
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